Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 21 Dec 2010 15:53:05 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/21/t12929469817ik2wh4yicbv2nw.htm/, Retrieved Sun, 05 May 2024 13:38:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113700, Retrieved Sun, 05 May 2024 13:38:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RM D  [Exponential Smoothing] [] [2010-11-27 13:17:09] [0175b38674e1402e67841c9c82e4a5a3]
-   PD      [Exponential Smoothing] [] [2010-12-21 15:53:05] [c2e23af56713b360851e64c7775b3f2b] [Current]
Feedback Forum

Post a new message
Dataseries X:
13.193
15.234
14.718
16.961
13.945
15.876
16.226
18.316
16.748
17.904
17.209
18.950
17.225
18.710
17.236
18.687
17.580
19.568
17.381
19.580
17.260
18.661
15.658
18.674
15.908
17.475
17.725
19.562
16.368
19.555
17.743
19.867
15.703
19.324
18.162
19.074
15.323
19.704
18.375
18.352
13.927
17.795
16.761
18.902
16.239
19.158
18.279
15.698
16.239
18.431
18.414
19.801
14.995
18.706
18.232
19.409
16.263
19.017
20.298
19.891
15.203
17.845
17.502
18.532
15.737
17.770
17.224
17.601
14.940
18.507
17.635
19.392
15.699
17.661
18.243
19.643
15.770
17.344
17.229
17.322
16.152
17.919
16.918
18.114
16.308
17.759
16.021
17.952
15.954
17.762
16.610
17.751
15.458
18.106
15.990
15.349
13.185
15.409
16.007
16.633
14.800
15.974
15.693




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113700&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113700&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113700&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.29732040102439
beta0.0796850294543876
gamma0.343463420691937

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.29732040102439 \tabularnewline
beta & 0.0796850294543876 \tabularnewline
gamma & 0.343463420691937 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113700&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.29732040102439[/C][/ROW]
[ROW][C]beta[/C][C]0.0796850294543876[/C][/ROW]
[ROW][C]gamma[/C][C]0.343463420691937[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113700&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113700&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.29732040102439
beta0.0796850294543876
gamma0.343463420691937







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
513.94513.555856250.389143749999999
615.87615.52103871366010.35496128633987
716.22615.55421777095750.671782229042499
818.31618.12338501242740.192614987572554
916.74815.29506728555161.45293271444844
1017.90417.63159803617210.272401963827942
1117.20917.7780494792103-0.569049479210292
1218.9519.8946057697566-0.944605769756588
1317.22517.03735526959420.187644730405818
1418.7118.68781312585180.0221868741482361
1517.23618.5259004693103-1.28990046931032
1618.68720.2895259586921-1.60252595869208
1717.5817.44636906914960.133630930850373
1819.56818.97599944756670.592000552433277
1917.38118.6155029721445-1.23450297214455
2019.5820.2701255540762-0.690125554076211
2117.2618.0888496297511-0.828849629751115
2218.66119.3917303036948-0.730730303694774
2315.65818.1145941295205-2.4565941295205
2418.67419.4257451246555-0.751745124655493
2515.90817.079706649638-1.17170664963801
2617.47518.1832450872427-0.708245087242666
2717.72516.3757143591471.34928564085300
2819.56219.19950452419430.362495475805666
2916.36817.0794127110294-0.711412711029414
3019.55518.43858091798281.11641908201720
3117.74317.72028518561720.022714814382784
3219.86719.9302239672163-0.0632239672162811
3315.70317.4330106503664-1.73001065036636
3419.32418.91496955160270.40903044839731
3518.16217.69013659105260.47186340894735
3619.07419.9912603765896-0.917260376589631
3715.32316.7960054342244-1.47300543422443
3819.70418.83486352692060.86913647307938
3918.37517.73713468603480.637865313965168
4018.35219.7314302295545-1.3794302295545
4113.92716.2327606163285-2.30576061632854
4217.79518.5376816086575-0.742681608657453
4316.76116.8151174998679-0.0541174998679175
4418.90218.01062153143570.89137846856428
4516.23914.91115743286081.32784256713923
4619.15818.70736367439710.450636325602876
4718.27917.56775072662910.711249273370886
4815.69819.2991095189821-3.60110951898208
4916.23914.94294457393671.29605542606332
5018.43118.4909068080669-0.0599068080669376
5118.41417.22321682390871.19078317609126
5219.80118.02856712159591.77243287840412
5314.99516.5514622356321-1.55646223563213
5418.70618.9559679026148-0.249967902614841
5518.23217.96102287952150.270977120478491
5619.40918.63888869060020.770111309399816
5716.26316.04222936807130.220770631928687
5819.01719.3144318674623-0.297431867462297
5920.29818.45395137432761.84404862567244
6019.89119.78010522748560.110894772514438
6115.20316.8993671302384-1.69636713023842
6217.84519.4755794482686-1.63057944826864
6317.50218.7030565532131-1.20105655321313
6418.53218.6009008849753-0.0689008849753279
6515.73715.1216229384220.615377061577998
6617.7718.3469015054496-0.576901505449644
6717.22417.9621453996123-0.738145399612318
6817.60118.2526535090336-0.651653509033636
6914.9414.73324266833590.206757331664102
7018.50717.50758354920800.999416450791983
7117.63517.54823312103700.0867668789629548
7219.39218.12007220820621.27192779179382
7315.69915.44052109602880.258478903971151
7417.66118.4835361749248-0.82253617492475
7518.24317.78104542626460.461954573735373
7619.64318.77818329863640.864816701363612
7715.7715.75106940543790.0189305945621268
7817.34418.4743594168996-1.13035941689960
7917.22917.9954535127495-0.766453512749543
8017.32218.7005877194464-1.37858771944638
8116.15214.72516152336271.42683847663727
8217.91917.54588006630420.373119933695754
8316.91817.5936403239496-0.675640323949565
8418.11418.1720156218748-0.0580156218748336
8516.30815.29156012560151.01643987439847
8617.75917.75148902952990.00751097047010418
8716.02117.4443111756237-1.42331117562367
8817.95217.93861300427160.0133869957284318
8915.95415.32955666947650.624443330523471
9017.76217.41100567044590.350994329554119
9116.6116.8503371815392-0.240337181539221
9217.75118.0608340112344-0.309834011234361
9315.45815.5132281152180-0.0552281152180303
9418.10617.32057409277300.785425907226966
9515.9916.7506214131922-0.76062141319222
9615.34917.7815930535876-2.43259305358758
9713.18514.6059416273707-1.42094162737071
9815.40916.1194103233798-0.71041032337981
9916.00714.60543508202871.4015649179713
10016.63315.80082420951020.832175790489819
10114.813.84243770729980.957562292700159
10215.97416.2933444064655-0.319344406465540
10315.69315.47339755285030.219602447149711

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 13.945 & 13.55585625 & 0.389143749999999 \tabularnewline
6 & 15.876 & 15.5210387136601 & 0.35496128633987 \tabularnewline
7 & 16.226 & 15.5542177709575 & 0.671782229042499 \tabularnewline
8 & 18.316 & 18.1233850124274 & 0.192614987572554 \tabularnewline
9 & 16.748 & 15.2950672855516 & 1.45293271444844 \tabularnewline
10 & 17.904 & 17.6315980361721 & 0.272401963827942 \tabularnewline
11 & 17.209 & 17.7780494792103 & -0.569049479210292 \tabularnewline
12 & 18.95 & 19.8946057697566 & -0.944605769756588 \tabularnewline
13 & 17.225 & 17.0373552695942 & 0.187644730405818 \tabularnewline
14 & 18.71 & 18.6878131258518 & 0.0221868741482361 \tabularnewline
15 & 17.236 & 18.5259004693103 & -1.28990046931032 \tabularnewline
16 & 18.687 & 20.2895259586921 & -1.60252595869208 \tabularnewline
17 & 17.58 & 17.4463690691496 & 0.133630930850373 \tabularnewline
18 & 19.568 & 18.9759994475667 & 0.592000552433277 \tabularnewline
19 & 17.381 & 18.6155029721445 & -1.23450297214455 \tabularnewline
20 & 19.58 & 20.2701255540762 & -0.690125554076211 \tabularnewline
21 & 17.26 & 18.0888496297511 & -0.828849629751115 \tabularnewline
22 & 18.661 & 19.3917303036948 & -0.730730303694774 \tabularnewline
23 & 15.658 & 18.1145941295205 & -2.4565941295205 \tabularnewline
24 & 18.674 & 19.4257451246555 & -0.751745124655493 \tabularnewline
25 & 15.908 & 17.079706649638 & -1.17170664963801 \tabularnewline
26 & 17.475 & 18.1832450872427 & -0.708245087242666 \tabularnewline
27 & 17.725 & 16.375714359147 & 1.34928564085300 \tabularnewline
28 & 19.562 & 19.1995045241943 & 0.362495475805666 \tabularnewline
29 & 16.368 & 17.0794127110294 & -0.711412711029414 \tabularnewline
30 & 19.555 & 18.4385809179828 & 1.11641908201720 \tabularnewline
31 & 17.743 & 17.7202851856172 & 0.022714814382784 \tabularnewline
32 & 19.867 & 19.9302239672163 & -0.0632239672162811 \tabularnewline
33 & 15.703 & 17.4330106503664 & -1.73001065036636 \tabularnewline
34 & 19.324 & 18.9149695516027 & 0.40903044839731 \tabularnewline
35 & 18.162 & 17.6901365910526 & 0.47186340894735 \tabularnewline
36 & 19.074 & 19.9912603765896 & -0.917260376589631 \tabularnewline
37 & 15.323 & 16.7960054342244 & -1.47300543422443 \tabularnewline
38 & 19.704 & 18.8348635269206 & 0.86913647307938 \tabularnewline
39 & 18.375 & 17.7371346860348 & 0.637865313965168 \tabularnewline
40 & 18.352 & 19.7314302295545 & -1.3794302295545 \tabularnewline
41 & 13.927 & 16.2327606163285 & -2.30576061632854 \tabularnewline
42 & 17.795 & 18.5376816086575 & -0.742681608657453 \tabularnewline
43 & 16.761 & 16.8151174998679 & -0.0541174998679175 \tabularnewline
44 & 18.902 & 18.0106215314357 & 0.89137846856428 \tabularnewline
45 & 16.239 & 14.9111574328608 & 1.32784256713923 \tabularnewline
46 & 19.158 & 18.7073636743971 & 0.450636325602876 \tabularnewline
47 & 18.279 & 17.5677507266291 & 0.711249273370886 \tabularnewline
48 & 15.698 & 19.2991095189821 & -3.60110951898208 \tabularnewline
49 & 16.239 & 14.9429445739367 & 1.29605542606332 \tabularnewline
50 & 18.431 & 18.4909068080669 & -0.0599068080669376 \tabularnewline
51 & 18.414 & 17.2232168239087 & 1.19078317609126 \tabularnewline
52 & 19.801 & 18.0285671215959 & 1.77243287840412 \tabularnewline
53 & 14.995 & 16.5514622356321 & -1.55646223563213 \tabularnewline
54 & 18.706 & 18.9559679026148 & -0.249967902614841 \tabularnewline
55 & 18.232 & 17.9610228795215 & 0.270977120478491 \tabularnewline
56 & 19.409 & 18.6388886906002 & 0.770111309399816 \tabularnewline
57 & 16.263 & 16.0422293680713 & 0.220770631928687 \tabularnewline
58 & 19.017 & 19.3144318674623 & -0.297431867462297 \tabularnewline
59 & 20.298 & 18.4539513743276 & 1.84404862567244 \tabularnewline
60 & 19.891 & 19.7801052274856 & 0.110894772514438 \tabularnewline
61 & 15.203 & 16.8993671302384 & -1.69636713023842 \tabularnewline
62 & 17.845 & 19.4755794482686 & -1.63057944826864 \tabularnewline
63 & 17.502 & 18.7030565532131 & -1.20105655321313 \tabularnewline
64 & 18.532 & 18.6009008849753 & -0.0689008849753279 \tabularnewline
65 & 15.737 & 15.121622938422 & 0.615377061577998 \tabularnewline
66 & 17.77 & 18.3469015054496 & -0.576901505449644 \tabularnewline
67 & 17.224 & 17.9621453996123 & -0.738145399612318 \tabularnewline
68 & 17.601 & 18.2526535090336 & -0.651653509033636 \tabularnewline
69 & 14.94 & 14.7332426683359 & 0.206757331664102 \tabularnewline
70 & 18.507 & 17.5075835492080 & 0.999416450791983 \tabularnewline
71 & 17.635 & 17.5482331210370 & 0.0867668789629548 \tabularnewline
72 & 19.392 & 18.1200722082062 & 1.27192779179382 \tabularnewline
73 & 15.699 & 15.4405210960288 & 0.258478903971151 \tabularnewline
74 & 17.661 & 18.4835361749248 & -0.82253617492475 \tabularnewline
75 & 18.243 & 17.7810454262646 & 0.461954573735373 \tabularnewline
76 & 19.643 & 18.7781832986364 & 0.864816701363612 \tabularnewline
77 & 15.77 & 15.7510694054379 & 0.0189305945621268 \tabularnewline
78 & 17.344 & 18.4743594168996 & -1.13035941689960 \tabularnewline
79 & 17.229 & 17.9954535127495 & -0.766453512749543 \tabularnewline
80 & 17.322 & 18.7005877194464 & -1.37858771944638 \tabularnewline
81 & 16.152 & 14.7251615233627 & 1.42683847663727 \tabularnewline
82 & 17.919 & 17.5458800663042 & 0.373119933695754 \tabularnewline
83 & 16.918 & 17.5936403239496 & -0.675640323949565 \tabularnewline
84 & 18.114 & 18.1720156218748 & -0.0580156218748336 \tabularnewline
85 & 16.308 & 15.2915601256015 & 1.01643987439847 \tabularnewline
86 & 17.759 & 17.7514890295299 & 0.00751097047010418 \tabularnewline
87 & 16.021 & 17.4443111756237 & -1.42331117562367 \tabularnewline
88 & 17.952 & 17.9386130042716 & 0.0133869957284318 \tabularnewline
89 & 15.954 & 15.3295566694765 & 0.624443330523471 \tabularnewline
90 & 17.762 & 17.4110056704459 & 0.350994329554119 \tabularnewline
91 & 16.61 & 16.8503371815392 & -0.240337181539221 \tabularnewline
92 & 17.751 & 18.0608340112344 & -0.309834011234361 \tabularnewline
93 & 15.458 & 15.5132281152180 & -0.0552281152180303 \tabularnewline
94 & 18.106 & 17.3205740927730 & 0.785425907226966 \tabularnewline
95 & 15.99 & 16.7506214131922 & -0.76062141319222 \tabularnewline
96 & 15.349 & 17.7815930535876 & -2.43259305358758 \tabularnewline
97 & 13.185 & 14.6059416273707 & -1.42094162737071 \tabularnewline
98 & 15.409 & 16.1194103233798 & -0.71041032337981 \tabularnewline
99 & 16.007 & 14.6054350820287 & 1.4015649179713 \tabularnewline
100 & 16.633 & 15.8008242095102 & 0.832175790489819 \tabularnewline
101 & 14.8 & 13.8424377072998 & 0.957562292700159 \tabularnewline
102 & 15.974 & 16.2933444064655 & -0.319344406465540 \tabularnewline
103 & 15.693 & 15.4733975528503 & 0.219602447149711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113700&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]5[/C][C]13.945[/C][C]13.55585625[/C][C]0.389143749999999[/C][/ROW]
[ROW][C]6[/C][C]15.876[/C][C]15.5210387136601[/C][C]0.35496128633987[/C][/ROW]
[ROW][C]7[/C][C]16.226[/C][C]15.5542177709575[/C][C]0.671782229042499[/C][/ROW]
[ROW][C]8[/C][C]18.316[/C][C]18.1233850124274[/C][C]0.192614987572554[/C][/ROW]
[ROW][C]9[/C][C]16.748[/C][C]15.2950672855516[/C][C]1.45293271444844[/C][/ROW]
[ROW][C]10[/C][C]17.904[/C][C]17.6315980361721[/C][C]0.272401963827942[/C][/ROW]
[ROW][C]11[/C][C]17.209[/C][C]17.7780494792103[/C][C]-0.569049479210292[/C][/ROW]
[ROW][C]12[/C][C]18.95[/C][C]19.8946057697566[/C][C]-0.944605769756588[/C][/ROW]
[ROW][C]13[/C][C]17.225[/C][C]17.0373552695942[/C][C]0.187644730405818[/C][/ROW]
[ROW][C]14[/C][C]18.71[/C][C]18.6878131258518[/C][C]0.0221868741482361[/C][/ROW]
[ROW][C]15[/C][C]17.236[/C][C]18.5259004693103[/C][C]-1.28990046931032[/C][/ROW]
[ROW][C]16[/C][C]18.687[/C][C]20.2895259586921[/C][C]-1.60252595869208[/C][/ROW]
[ROW][C]17[/C][C]17.58[/C][C]17.4463690691496[/C][C]0.133630930850373[/C][/ROW]
[ROW][C]18[/C][C]19.568[/C][C]18.9759994475667[/C][C]0.592000552433277[/C][/ROW]
[ROW][C]19[/C][C]17.381[/C][C]18.6155029721445[/C][C]-1.23450297214455[/C][/ROW]
[ROW][C]20[/C][C]19.58[/C][C]20.2701255540762[/C][C]-0.690125554076211[/C][/ROW]
[ROW][C]21[/C][C]17.26[/C][C]18.0888496297511[/C][C]-0.828849629751115[/C][/ROW]
[ROW][C]22[/C][C]18.661[/C][C]19.3917303036948[/C][C]-0.730730303694774[/C][/ROW]
[ROW][C]23[/C][C]15.658[/C][C]18.1145941295205[/C][C]-2.4565941295205[/C][/ROW]
[ROW][C]24[/C][C]18.674[/C][C]19.4257451246555[/C][C]-0.751745124655493[/C][/ROW]
[ROW][C]25[/C][C]15.908[/C][C]17.079706649638[/C][C]-1.17170664963801[/C][/ROW]
[ROW][C]26[/C][C]17.475[/C][C]18.1832450872427[/C][C]-0.708245087242666[/C][/ROW]
[ROW][C]27[/C][C]17.725[/C][C]16.375714359147[/C][C]1.34928564085300[/C][/ROW]
[ROW][C]28[/C][C]19.562[/C][C]19.1995045241943[/C][C]0.362495475805666[/C][/ROW]
[ROW][C]29[/C][C]16.368[/C][C]17.0794127110294[/C][C]-0.711412711029414[/C][/ROW]
[ROW][C]30[/C][C]19.555[/C][C]18.4385809179828[/C][C]1.11641908201720[/C][/ROW]
[ROW][C]31[/C][C]17.743[/C][C]17.7202851856172[/C][C]0.022714814382784[/C][/ROW]
[ROW][C]32[/C][C]19.867[/C][C]19.9302239672163[/C][C]-0.0632239672162811[/C][/ROW]
[ROW][C]33[/C][C]15.703[/C][C]17.4330106503664[/C][C]-1.73001065036636[/C][/ROW]
[ROW][C]34[/C][C]19.324[/C][C]18.9149695516027[/C][C]0.40903044839731[/C][/ROW]
[ROW][C]35[/C][C]18.162[/C][C]17.6901365910526[/C][C]0.47186340894735[/C][/ROW]
[ROW][C]36[/C][C]19.074[/C][C]19.9912603765896[/C][C]-0.917260376589631[/C][/ROW]
[ROW][C]37[/C][C]15.323[/C][C]16.7960054342244[/C][C]-1.47300543422443[/C][/ROW]
[ROW][C]38[/C][C]19.704[/C][C]18.8348635269206[/C][C]0.86913647307938[/C][/ROW]
[ROW][C]39[/C][C]18.375[/C][C]17.7371346860348[/C][C]0.637865313965168[/C][/ROW]
[ROW][C]40[/C][C]18.352[/C][C]19.7314302295545[/C][C]-1.3794302295545[/C][/ROW]
[ROW][C]41[/C][C]13.927[/C][C]16.2327606163285[/C][C]-2.30576061632854[/C][/ROW]
[ROW][C]42[/C][C]17.795[/C][C]18.5376816086575[/C][C]-0.742681608657453[/C][/ROW]
[ROW][C]43[/C][C]16.761[/C][C]16.8151174998679[/C][C]-0.0541174998679175[/C][/ROW]
[ROW][C]44[/C][C]18.902[/C][C]18.0106215314357[/C][C]0.89137846856428[/C][/ROW]
[ROW][C]45[/C][C]16.239[/C][C]14.9111574328608[/C][C]1.32784256713923[/C][/ROW]
[ROW][C]46[/C][C]19.158[/C][C]18.7073636743971[/C][C]0.450636325602876[/C][/ROW]
[ROW][C]47[/C][C]18.279[/C][C]17.5677507266291[/C][C]0.711249273370886[/C][/ROW]
[ROW][C]48[/C][C]15.698[/C][C]19.2991095189821[/C][C]-3.60110951898208[/C][/ROW]
[ROW][C]49[/C][C]16.239[/C][C]14.9429445739367[/C][C]1.29605542606332[/C][/ROW]
[ROW][C]50[/C][C]18.431[/C][C]18.4909068080669[/C][C]-0.0599068080669376[/C][/ROW]
[ROW][C]51[/C][C]18.414[/C][C]17.2232168239087[/C][C]1.19078317609126[/C][/ROW]
[ROW][C]52[/C][C]19.801[/C][C]18.0285671215959[/C][C]1.77243287840412[/C][/ROW]
[ROW][C]53[/C][C]14.995[/C][C]16.5514622356321[/C][C]-1.55646223563213[/C][/ROW]
[ROW][C]54[/C][C]18.706[/C][C]18.9559679026148[/C][C]-0.249967902614841[/C][/ROW]
[ROW][C]55[/C][C]18.232[/C][C]17.9610228795215[/C][C]0.270977120478491[/C][/ROW]
[ROW][C]56[/C][C]19.409[/C][C]18.6388886906002[/C][C]0.770111309399816[/C][/ROW]
[ROW][C]57[/C][C]16.263[/C][C]16.0422293680713[/C][C]0.220770631928687[/C][/ROW]
[ROW][C]58[/C][C]19.017[/C][C]19.3144318674623[/C][C]-0.297431867462297[/C][/ROW]
[ROW][C]59[/C][C]20.298[/C][C]18.4539513743276[/C][C]1.84404862567244[/C][/ROW]
[ROW][C]60[/C][C]19.891[/C][C]19.7801052274856[/C][C]0.110894772514438[/C][/ROW]
[ROW][C]61[/C][C]15.203[/C][C]16.8993671302384[/C][C]-1.69636713023842[/C][/ROW]
[ROW][C]62[/C][C]17.845[/C][C]19.4755794482686[/C][C]-1.63057944826864[/C][/ROW]
[ROW][C]63[/C][C]17.502[/C][C]18.7030565532131[/C][C]-1.20105655321313[/C][/ROW]
[ROW][C]64[/C][C]18.532[/C][C]18.6009008849753[/C][C]-0.0689008849753279[/C][/ROW]
[ROW][C]65[/C][C]15.737[/C][C]15.121622938422[/C][C]0.615377061577998[/C][/ROW]
[ROW][C]66[/C][C]17.77[/C][C]18.3469015054496[/C][C]-0.576901505449644[/C][/ROW]
[ROW][C]67[/C][C]17.224[/C][C]17.9621453996123[/C][C]-0.738145399612318[/C][/ROW]
[ROW][C]68[/C][C]17.601[/C][C]18.2526535090336[/C][C]-0.651653509033636[/C][/ROW]
[ROW][C]69[/C][C]14.94[/C][C]14.7332426683359[/C][C]0.206757331664102[/C][/ROW]
[ROW][C]70[/C][C]18.507[/C][C]17.5075835492080[/C][C]0.999416450791983[/C][/ROW]
[ROW][C]71[/C][C]17.635[/C][C]17.5482331210370[/C][C]0.0867668789629548[/C][/ROW]
[ROW][C]72[/C][C]19.392[/C][C]18.1200722082062[/C][C]1.27192779179382[/C][/ROW]
[ROW][C]73[/C][C]15.699[/C][C]15.4405210960288[/C][C]0.258478903971151[/C][/ROW]
[ROW][C]74[/C][C]17.661[/C][C]18.4835361749248[/C][C]-0.82253617492475[/C][/ROW]
[ROW][C]75[/C][C]18.243[/C][C]17.7810454262646[/C][C]0.461954573735373[/C][/ROW]
[ROW][C]76[/C][C]19.643[/C][C]18.7781832986364[/C][C]0.864816701363612[/C][/ROW]
[ROW][C]77[/C][C]15.77[/C][C]15.7510694054379[/C][C]0.0189305945621268[/C][/ROW]
[ROW][C]78[/C][C]17.344[/C][C]18.4743594168996[/C][C]-1.13035941689960[/C][/ROW]
[ROW][C]79[/C][C]17.229[/C][C]17.9954535127495[/C][C]-0.766453512749543[/C][/ROW]
[ROW][C]80[/C][C]17.322[/C][C]18.7005877194464[/C][C]-1.37858771944638[/C][/ROW]
[ROW][C]81[/C][C]16.152[/C][C]14.7251615233627[/C][C]1.42683847663727[/C][/ROW]
[ROW][C]82[/C][C]17.919[/C][C]17.5458800663042[/C][C]0.373119933695754[/C][/ROW]
[ROW][C]83[/C][C]16.918[/C][C]17.5936403239496[/C][C]-0.675640323949565[/C][/ROW]
[ROW][C]84[/C][C]18.114[/C][C]18.1720156218748[/C][C]-0.0580156218748336[/C][/ROW]
[ROW][C]85[/C][C]16.308[/C][C]15.2915601256015[/C][C]1.01643987439847[/C][/ROW]
[ROW][C]86[/C][C]17.759[/C][C]17.7514890295299[/C][C]0.00751097047010418[/C][/ROW]
[ROW][C]87[/C][C]16.021[/C][C]17.4443111756237[/C][C]-1.42331117562367[/C][/ROW]
[ROW][C]88[/C][C]17.952[/C][C]17.9386130042716[/C][C]0.0133869957284318[/C][/ROW]
[ROW][C]89[/C][C]15.954[/C][C]15.3295566694765[/C][C]0.624443330523471[/C][/ROW]
[ROW][C]90[/C][C]17.762[/C][C]17.4110056704459[/C][C]0.350994329554119[/C][/ROW]
[ROW][C]91[/C][C]16.61[/C][C]16.8503371815392[/C][C]-0.240337181539221[/C][/ROW]
[ROW][C]92[/C][C]17.751[/C][C]18.0608340112344[/C][C]-0.309834011234361[/C][/ROW]
[ROW][C]93[/C][C]15.458[/C][C]15.5132281152180[/C][C]-0.0552281152180303[/C][/ROW]
[ROW][C]94[/C][C]18.106[/C][C]17.3205740927730[/C][C]0.785425907226966[/C][/ROW]
[ROW][C]95[/C][C]15.99[/C][C]16.7506214131922[/C][C]-0.76062141319222[/C][/ROW]
[ROW][C]96[/C][C]15.349[/C][C]17.7815930535876[/C][C]-2.43259305358758[/C][/ROW]
[ROW][C]97[/C][C]13.185[/C][C]14.6059416273707[/C][C]-1.42094162737071[/C][/ROW]
[ROW][C]98[/C][C]15.409[/C][C]16.1194103233798[/C][C]-0.71041032337981[/C][/ROW]
[ROW][C]99[/C][C]16.007[/C][C]14.6054350820287[/C][C]1.4015649179713[/C][/ROW]
[ROW][C]100[/C][C]16.633[/C][C]15.8008242095102[/C][C]0.832175790489819[/C][/ROW]
[ROW][C]101[/C][C]14.8[/C][C]13.8424377072998[/C][C]0.957562292700159[/C][/ROW]
[ROW][C]102[/C][C]15.974[/C][C]16.2933444064655[/C][C]-0.319344406465540[/C][/ROW]
[ROW][C]103[/C][C]15.693[/C][C]15.4733975528503[/C][C]0.219602447149711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113700&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113700&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
513.94513.555856250.389143749999999
615.87615.52103871366010.35496128633987
716.22615.55421777095750.671782229042499
818.31618.12338501242740.192614987572554
916.74815.29506728555161.45293271444844
1017.90417.63159803617210.272401963827942
1117.20917.7780494792103-0.569049479210292
1218.9519.8946057697566-0.944605769756588
1317.22517.03735526959420.187644730405818
1418.7118.68781312585180.0221868741482361
1517.23618.5259004693103-1.28990046931032
1618.68720.2895259586921-1.60252595869208
1717.5817.44636906914960.133630930850373
1819.56818.97599944756670.592000552433277
1917.38118.6155029721445-1.23450297214455
2019.5820.2701255540762-0.690125554076211
2117.2618.0888496297511-0.828849629751115
2218.66119.3917303036948-0.730730303694774
2315.65818.1145941295205-2.4565941295205
2418.67419.4257451246555-0.751745124655493
2515.90817.079706649638-1.17170664963801
2617.47518.1832450872427-0.708245087242666
2717.72516.3757143591471.34928564085300
2819.56219.19950452419430.362495475805666
2916.36817.0794127110294-0.711412711029414
3019.55518.43858091798281.11641908201720
3117.74317.72028518561720.022714814382784
3219.86719.9302239672163-0.0632239672162811
3315.70317.4330106503664-1.73001065036636
3419.32418.91496955160270.40903044839731
3518.16217.69013659105260.47186340894735
3619.07419.9912603765896-0.917260376589631
3715.32316.7960054342244-1.47300543422443
3819.70418.83486352692060.86913647307938
3918.37517.73713468603480.637865313965168
4018.35219.7314302295545-1.3794302295545
4113.92716.2327606163285-2.30576061632854
4217.79518.5376816086575-0.742681608657453
4316.76116.8151174998679-0.0541174998679175
4418.90218.01062153143570.89137846856428
4516.23914.91115743286081.32784256713923
4619.15818.70736367439710.450636325602876
4718.27917.56775072662910.711249273370886
4815.69819.2991095189821-3.60110951898208
4916.23914.94294457393671.29605542606332
5018.43118.4909068080669-0.0599068080669376
5118.41417.22321682390871.19078317609126
5219.80118.02856712159591.77243287840412
5314.99516.5514622356321-1.55646223563213
5418.70618.9559679026148-0.249967902614841
5518.23217.96102287952150.270977120478491
5619.40918.63888869060020.770111309399816
5716.26316.04222936807130.220770631928687
5819.01719.3144318674623-0.297431867462297
5920.29818.45395137432761.84404862567244
6019.89119.78010522748560.110894772514438
6115.20316.8993671302384-1.69636713023842
6217.84519.4755794482686-1.63057944826864
6317.50218.7030565532131-1.20105655321313
6418.53218.6009008849753-0.0689008849753279
6515.73715.1216229384220.615377061577998
6617.7718.3469015054496-0.576901505449644
6717.22417.9621453996123-0.738145399612318
6817.60118.2526535090336-0.651653509033636
6914.9414.73324266833590.206757331664102
7018.50717.50758354920800.999416450791983
7117.63517.54823312103700.0867668789629548
7219.39218.12007220820621.27192779179382
7315.69915.44052109602880.258478903971151
7417.66118.4835361749248-0.82253617492475
7518.24317.78104542626460.461954573735373
7619.64318.77818329863640.864816701363612
7715.7715.75106940543790.0189305945621268
7817.34418.4743594168996-1.13035941689960
7917.22917.9954535127495-0.766453512749543
8017.32218.7005877194464-1.37858771944638
8116.15214.72516152336271.42683847663727
8217.91917.54588006630420.373119933695754
8316.91817.5936403239496-0.675640323949565
8418.11418.1720156218748-0.0580156218748336
8516.30815.29156012560151.01643987439847
8617.75917.75148902952990.00751097047010418
8716.02117.4443111756237-1.42331117562367
8817.95217.93861300427160.0133869957284318
8915.95415.32955666947650.624443330523471
9017.76217.41100567044590.350994329554119
9116.6116.8503371815392-0.240337181539221
9217.75118.0608340112344-0.309834011234361
9315.45815.5132281152180-0.0552281152180303
9418.10617.32057409277300.785425907226966
9515.9916.7506214131922-0.76062141319222
9615.34917.7815930535876-2.43259305358758
9713.18514.6059416273707-1.42094162737071
9815.40916.1194103233798-0.71041032337981
9916.00714.60543508202871.4015649179713
10016.63315.80082420951020.832175790489819
10114.813.84243770729980.957562292700159
10215.97416.2933444064655-0.319344406465540
10315.69315.47339755285030.219602447149711







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10416.219985416982214.208148105789618.2318227281749
10514.064760914031611.951805897029516.1777159310337
10615.920427009657513.696577631674718.1442763876402
10715.330702568469012.986600476693517.6748046602446

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
104 & 16.2199854169822 & 14.2081481057896 & 18.2318227281749 \tabularnewline
105 & 14.0647609140316 & 11.9518058970295 & 16.1777159310337 \tabularnewline
106 & 15.9204270096575 & 13.6965776316747 & 18.1442763876402 \tabularnewline
107 & 15.3307025684690 & 12.9866004766935 & 17.6748046602446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113700&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]104[/C][C]16.2199854169822[/C][C]14.2081481057896[/C][C]18.2318227281749[/C][/ROW]
[ROW][C]105[/C][C]14.0647609140316[/C][C]11.9518058970295[/C][C]16.1777159310337[/C][/ROW]
[ROW][C]106[/C][C]15.9204270096575[/C][C]13.6965776316747[/C][C]18.1442763876402[/C][/ROW]
[ROW][C]107[/C][C]15.3307025684690[/C][C]12.9866004766935[/C][C]17.6748046602446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113700&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113700&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10416.219985416982214.208148105789618.2318227281749
10514.064760914031611.951805897029516.1777159310337
10615.920427009657513.696577631674718.1442763876402
10715.330702568469012.986600476693517.6748046602446



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 4 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')